Geodesic
The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in Cn
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 381-392

Voir la notice de l'article provenant de la source Cambridge University Press

Let ${{B}_{p1,p2}}\,=\,\left\{ z\,\in \,{{\mathbb{C}}^{n}}\,:\,{{\left| {{z}_{1}} \right|}^{{{p}_{1}}}}\,+\,{{\left| {{z}_{2}} \right|}^{{{p}_{2}}}}\,+\,\cdots \,+\,{{\left| {{z}_{n}} \right|}^{{{p}_{2}}}}\,<\,1 \right\}$ be an egg domain in ${{\mathbb{C}}^{n}}$ . In this paper, we first characterize the Kobayashi metric on ${{B}_{{{p}_{1}},{{p}_{2}}}}\,\left( {{p}_{1}}\,\ge 1,\,{{p}_{2}}\,>\,1 \right)$ and then establish a new type of classical boundary Schwarz lemma at ${{z}_{0}}\in \partial {{B}_{{{p}_{1}},{{p}_{2}}}}$ for holomorphic self-mappings of ${{B}_{{{p}_{1}},{{p}_{2}}}}\,\left( {{p}_{1}}\,\ge \,1,\,{{p}_{2}}\,>\,1 \right)$ ), where ${{z}_{0}}={{\left( {{e}^{i\theta }},\,0,\ldots ,0 \right)}^{\prime }}$ and $\theta \,\in \,\mathbb{R}$ .
DOI : 10.4153/CMB-2014-067-7
Mots-clés : 32H02, 30C80, 32A30, holomorphic mapping, Schwarz lemma, Kobayashi metric, egg domain 
Tang, Xiaomin; Liu, Taishun. The Schwarz Lemma at the Boundary of the Egg Domain Bp1,p2 in Cn. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 381-392. doi: 10.4153/CMB-2014-067-7
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